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Why random portfolios appear to outperform benchmarks...
11 responses

This is certainly interesting based off of scanning the first page. I remember that I use to try to implement a momentum strategy and found it to be delivering negative premia over time. So the logical thinking would be to invert it (into a mean-revert strategy) and have it deliver AMAZING alpha. obviously that was not the case. Reading this article will definitely allow me to understand more of this phenomenon

I just read the article I'm still not sure how a strategy and it's inverse can have negative returns, can you please elaborate?

Ari, the authors argue that through the Fama-French decomposition, they found that even if you invert each strategy, the outperformance is the result of having more exposure to value based portfolios.

So they talk about a long-only strategy, and its 'inverse', which is also long only. (That wouldn't be my intuitive understanding of an inverse strategy from a time-series point of view - I'd expect it go short where it went long - but from a weighting point of view it does make sense). They use either 1/w (and normalise) or max(w)-w (and normalise).

I assume when they are talking about price they are literally referring to the stock price?

@James.. Inverse strategy ' inverse' ETF... how does it woks...? and how come.. there is no sample algo in quantopian using inverse strategy... they seem.. to outperform the benchmark.

@James
I believe that you surmise correctly regarding the weighting vs. inverse weighting (long only) as opposed to inverse positions (long and short). However, raw price alone is not used as a criteria for weighting. There are numerous criteria used for weighting as shown in Exhibit 1. They use that table to show that capitalization weighting (as in market indices) is a poor choice which under-performs NUMEROUS other portfolio weighting criteria.

@Rob
Exhibit 1 is very interesting, I hadn't fully appreciated it. For the "High Risk = High Reward" strategies, the one which stands out to me is the "Inverse-Ratio of Market Beta Weighted" strategy which manages to have higher returns and lower standard deviation than the original strategy. I suppose some middle-ground between that and the "Minimum Variance" strategy would be ideal.

But what I mean is, in Appendix A, the last 4 paragraphs refer to price: "By design, a cap-weighted portfolio has larger allocations to the higher-price stocks, which have lower returns."
If that were the case, I could just select low-priced stocks, no? Am I missing something?

@JOHN
Perhaps there should be.

If that were the case, I could just select low-priced stocks, no? Am I missing somethin

Indeed. You are referring to the small-cap anomaly. http://ftalphaville.ft.com/2015/02/11/2118836/size-matters-if-you-control-your-junk/

@James
Exhibit 1 does have a nice shopping list of algos for experimentation.

The author appears to be using the term "price" loosely. I believe that he always means price in relationship to something else throughout the article. He seems to be using the term "price" as a proxy for capitalization in Appendix A as indicated in parenthesis since price x shares = capitalization. However, it seems obvious that price alone would not a good proxy for capitalization due to differences in the number of shares outstanding. After all, when a stock splits 2:1, the company's capitalization remains the same even though its shares are now half the price.

@Simon
Thank you that has made good reading.

@Rob
Hmm, perhaps he just means 'on average'? Stocks tend to split in order to keep in a sensible price range...

Interesting